Solve x^3+1+7x^2+x^2+15

$$x ^ { 3 } + 1 + 7 x ^ { 2 } + x ^ { 2 } + 15$$

Evaluate

$$x^{3}+8x^{2}+16$$

Solution Steps

Combine 7x^{2} and x^{2} to get 8x^{2}.

$$x^{3}+1+8x^{2}+15$$

Add 1 and 15 to get 16.

$$x^{3}+16+8x^{2}$$

Differentiate w.r.t. x

$$x\left(3x+16\right)$$

Steps Using Derivative Rule for Sum

Combine 7x^{2} and x^{2} to get 8x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+1+8x^{2}+15)$$

Add 1 and 15 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+16+8x^{2})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3x^{3-1}+2\times 8x^{2-1}$$

Subtract 1 from 3.

$$3x^{2}+2\times 8x^{2-1}$$

Multiply 2 times 8.

$$3x^{2}+16x^{2-1}$$

Subtract 1 from 2.

$$3x^{2}+16x^{1}$$

For any term t, t^{1}=t.

$$3x^{2}+16x$$